Dark Matter and Alternatives Non-Perturbative Eﬀects of Rotation in Gravitationally Bound Systems

Dark Matter and Alternatives Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems

Herbert Balasin, Daniel Grumiller, Florian Preis

Institute for Theoretical Physics Vienna University of Technology

Ariadna Final Presentation at ESA-ESTEC, July 22nd 2008

ARIADNA ID 07/1301 AO/1-5582/07/NL/CB Outline

PART I: Introduction Historic Introduction Experimental Introduction Theoretical Introduction

Galactic Rotation Curves Status quo Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems

PART II: H. Balasin “Nonlinear eﬀects in gravitationally bound systems” PART III: F. Preis “Rotational Velocity in General Relativity”

D. Grumiller — Dark Matter and Alternatives 2/17 Outline

PART I: Introduction Historic Introduction Experimental Introduction Theoretical Introduction

Galactic Rotation Curves Status quo Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems

PART II: H. Balasin “Nonlinear eﬀects in gravitationally bound systems” PART III: F. Preis “Rotational Velocity in General Relativity”

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 3/17 I Observations deviate from tables: gravitational anomalies!

I Diﬀerent explanations: change law of gravitation or predict Dark Matter to account for anomalies

I 1845: John Couch Adams and especially Urbain Le Verrier predict new planet and calculate its position

I 1846: Observational conﬁrmation by Johann Gottfried Galle and Heinrich Louis d’Arrest

Discovery of Neptune was ﬁrst success of the Dark Matter concept!

Historic Introduction First Success of Dark Matter Neptune: I 1821: Alexis Bouvard published tables of orbit of Uranus

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 4/17 I Diﬀerent explanations: change law of gravitation or predict Dark Matter to account for anomalies

I 1845: John Couch Adams and especially Urbain Le Verrier predict new planet and calculate its position

I 1846: Observational conﬁrmation by Johann Gottfried Galle and Heinrich Louis d’Arrest

Discovery of Neptune was ﬁrst success of the Dark Matter concept!

Historic Introduction First Success of Dark Matter Neptune: I 1821: Alexis Bouvard published tables of orbit of Uranus

I Observations deviate from tables: gravitational anomalies!

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 4/17 I 1845: John Couch Adams and especially Urbain Le Verrier predict new planet and calculate its position

I 1846: Observational conﬁrmation by Johann Gottfried Galle and Heinrich Louis d’Arrest

Discovery of Neptune was ﬁrst success of the Dark Matter concept!

Historic Introduction First Success of Dark Matter Neptune: I 1821: Alexis Bouvard published tables of orbit of Uranus

I Observations deviate from tables: gravitational anomalies!

I Diﬀerent explanations: change law of gravitation or predict Dark Matter to account for anomalies

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 4/17 I 1846: Observational conﬁrmation by Johann Gottfried Galle and Heinrich Louis d’Arrest

Discovery of Neptune was ﬁrst success of the Dark Matter concept!

Historic Introduction First Success of Dark Matter Neptune: I 1821: Alexis Bouvard published tables of orbit of Uranus

I Observations deviate from tables: gravitational anomalies!

I Diﬀerent explanations: change law of gravitation or predict Dark Matter to account for anomalies

I 1845: John Couch Adams and especially Urbain Le Verrier predict new planet and calculate its position

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 4/17 Discovery of Neptune was ﬁrst success of the Dark Matter concept!

Historic Introduction First Success of Dark Matter Neptune: I 1821: Alexis Bouvard published tables of orbit of Uranus

I Observations deviate from tables: gravitational anomalies!

I Diﬀerent explanations: change law of gravitation or predict Dark Matter to account for anomalies

I 1845: John Couch Adams and especially Urbain Le Verrier predict new planet and calculate its position

I 1846: Observational conﬁrmation by Johann Gottfried Galle and Heinrich Louis d’Arrest

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 4/17 Historic Introduction First Success of Dark Matter Neptune: I 1821: Alexis Bouvard published tables of orbit of Uranus

I Observations deviate from tables: gravitational anomalies!

I Diﬀerent explanations: change law of gravitation or predict Dark Matter to account for anomalies

I 1845: John Couch Adams and especially Urbain Le Verrier predict new planet and calculate its position

I 1846: Observational conﬁrmation by Johann Gottfried Galle and Heinrich Louis d’Arrest

Discovery of Neptune was ﬁrst success of the Dark Matter concept!

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 4/17 I Observations deviate from tables: gravitational anomalies!

I Diﬀerent explanations: change law of gravitation or predict Dark Matter to account for anomalies

I 1859: Urbain Le Verrier predicts new planet and calculates its position

I 1860: Observational ‘conﬁrmation’ by Lescarbault

I 1915: Einstein explains perihelion shift of Mercury with General Relativity Non-discovery of Vulcan was ﬁrst failure of the Dark Matter concept!

Historic Introduction First Failure of Dark Matter Vulcan: I 1840: Fran¸coisArago suggests problem of Mercury orbit to Urbain Le Verrier

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 5/17 I Diﬀerent explanations: change law of gravitation or predict Dark Matter to account for anomalies

I 1859: Urbain Le Verrier predicts new planet and calculates its position

I 1860: Observational ‘conﬁrmation’ by Lescarbault

I 1915: Einstein explains perihelion shift of Mercury with General Relativity Non-discovery of Vulcan was ﬁrst failure of the Dark Matter concept!

Historic Introduction First Failure of Dark Matter Vulcan: I 1840: Fran¸coisArago suggests problem of Mercury orbit to Urbain Le Verrier

I Observations deviate from tables: gravitational anomalies!

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 5/17 I 1859: Urbain Le Verrier predicts new planet and calculates its position

I 1860: Observational ‘conﬁrmation’ by Lescarbault

I 1915: Einstein explains perihelion shift of Mercury with General Relativity Non-discovery of Vulcan was ﬁrst failure of the Dark Matter concept!

Historic Introduction First Failure of Dark Matter Vulcan: I 1840: Fran¸coisArago suggests problem of Mercury orbit to Urbain Le Verrier

I Observations deviate from tables: gravitational anomalies!

I Diﬀerent explanations: change law of gravitation or predict Dark Matter to account for anomalies

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 5/17 I 1860: Observational ‘conﬁrmation’ by Lescarbault

I 1915: Einstein explains perihelion shift of Mercury with General Relativity Non-discovery of Vulcan was ﬁrst failure of the Dark Matter concept!

Historic Introduction First Failure of Dark Matter Vulcan: I 1840: Fran¸coisArago suggests problem of Mercury orbit to Urbain Le Verrier

I Observations deviate from tables: gravitational anomalies!

I Diﬀerent explanations: change law of gravitation or predict Dark Matter to account for anomalies

I 1859: Urbain Le Verrier predicts new planet and calculates its position

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 5/17 I 1915: Einstein explains perihelion shift of Mercury with General Relativity Non-discovery of Vulcan was ﬁrst failure of the Dark Matter concept!

Historic Introduction First Failure of Dark Matter Vulcan: I 1840: Fran¸coisArago suggests problem of Mercury orbit to Urbain Le Verrier

I Observations deviate from tables: gravitational anomalies!

I Diﬀerent explanations: change law of gravitation or predict Dark Matter to account for anomalies

I 1859: Urbain Le Verrier predicts new planet and calculates its position

I 1860: Observational ‘conﬁrmation’ by Lescarbault

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 5/17 Non-discovery of Vulcan was ﬁrst failure of the Dark Matter concept!

Historic Introduction First Failure of Dark Matter Vulcan: I 1840: Fran¸coisArago suggests problem of Mercury orbit to Urbain Le Verrier

I Observations deviate from tables: gravitational anomalies!

I Diﬀerent explanations: change law of gravitation or predict Dark Matter to account for anomalies

I 1859: Urbain Le Verrier predicts new planet and calculates its position

I 1860: Observational ‘conﬁrmation’ by Lescarbault

I 1915: Einstein explains perihelion shift of Mercury with General Relativity

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 5/17 Historic Introduction First Failure of Dark Matter Vulcan: I 1840: Fran¸coisArago suggests problem of Mercury orbit to Urbain Le Verrier

I Observations deviate from tables: gravitational anomalies!

I Diﬀerent explanations: change law of gravitation or predict Dark Matter to account for anomalies

I 1859: Urbain Le Verrier predicts new planet and calculates its position

I 1860: Observational ‘conﬁrmation’ by Lescarbault

I 1915: Einstein explains perihelion shift of Mercury with General Relativity Non-discovery of Vulcan was ﬁrst failure of the Dark Matter concept!

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 5/17 Option 1: I Conservative with respect to theory I Progressive with respect to matter content I Approach stands or falls with independent discovery of ‘Dark Matter’ Option 2: I Progressive with respect to theory I Conservative with respect to matter content I Approach stands or falls with plausibility of theory/implementation

Main lesson: remain open-minded!

Historic Introduction Historic Lesson

Gravitational anomalies lead to two options

1. Predict Dark Matter 2. Modify Theory/Modify Implementation of Theory

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 6/17 Option 2: I Progressive with respect to theory I Conservative with respect to matter content I Approach stands or falls with plausibility of theory/implementation

Main lesson: remain open-minded!

Historic Introduction Historic Lesson

Gravitational anomalies lead to two options

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 6/17 Main lesson: remain open-minded!

Historic Introduction Historic Lesson

Gravitational anomalies lead to two options

1. Predict Dark Matter 2. Modify Theory/Modify Implementation of Theory Option 1: I Conservative with respect to theory I Progressive with respect to matter content I Approach stands or falls with independent discovery of ‘Dark Matter’ Option 2: I Progressive with respect to theory I Conservative with respect to matter content I Approach stands or falls with plausibility of theory/implementation

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 6/17 Historic Introduction Historic Lesson

Gravitational anomalies lead to two options

Main lesson: remain open-minded!

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 6/17 Experimental Introduction Standard Model of Cosmology and Particle Physics

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 7/17 Experimental Introduction Standard Model of Cosmology and Particle Physics

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 7/17 Experimental Introduction Gravitational Anomalies, Some Data

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 8/17 Experimental Introduction Gravitational Anomalies, Some Data

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 8/17 I Dark Energy (73% of our Universe!) I Dark Matter (23% of our Universe!) I Pioneer anomaly (is it for real?) I Fly-by anomaly, Increase of astronomical units, ... (fake or real?) Note intriguing coincidences: −9 −10 2 aPioneer ≈ aHubble ≈ aMOND ≈ aΛ ≈ 10 − 10 m/s | {z } | {z } | {z } |{z} Solar system Galaxies Galaxies Supernovae

Prize question: success or failure of ‘Dark Hypotheses’?

? ... and in case of failure: what are alternative explanations?!

Experimental Introduction Gravitational Anomalies, Summary Experimental anomalies discovered in recent decade:

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 9/17 I Dark Matter (23% of our Universe!) I Pioneer anomaly (is it for real?) I Fly-by anomaly, Increase of astronomical units, ... (fake or real?) Note intriguing coincidences: −9 −10 2 aPioneer ≈ aHubble ≈ aMOND ≈ aΛ ≈ 10 − 10 m/s | {z } | {z } | {z } |{z} Solar system Galaxies Galaxies Supernovae

Prize question: success or failure of ‘Dark Hypotheses’?

? ... and in case of failure: what are alternative explanations?!

Experimental Introduction Gravitational Anomalies, Summary Experimental anomalies discovered in recent decade:

I Dark Energy (73% of our Universe!)

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 9/17 I Pioneer anomaly (is it for real?) I Fly-by anomaly, Increase of astronomical units, ... (fake or real?) Note intriguing coincidences: −9 −10 2 aPioneer ≈ aHubble ≈ aMOND ≈ aΛ ≈ 10 − 10 m/s | {z } | {z } | {z } |{z} Solar system Galaxies Galaxies Supernovae

Prize question: success or failure of ‘Dark Hypotheses’?

? ... and in case of failure: what are alternative explanations?!

Experimental Introduction Gravitational Anomalies, Summary Experimental anomalies discovered in recent decade:

I Dark Energy (73% of our Universe!) I Dark Matter (23% of our Universe!)

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 9/17 I Fly-by anomaly, Increase of astronomical units, ... (fake or real?) Note intriguing coincidences: −9 −10 2 aPioneer ≈ aHubble ≈ aMOND ≈ aΛ ≈ 10 − 10 m/s | {z } | {z } | {z } |{z} Solar system Galaxies Galaxies Supernovae

Prize question: success or failure of ‘Dark Hypotheses’?

? ... and in case of failure: what are alternative explanations?!

Experimental Introduction Gravitational Anomalies, Summary Experimental anomalies discovered in recent decade:

I Dark Energy (73% of our Universe!) I Dark Matter (23% of our Universe!) I Pioneer anomaly (is it for real?)

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 9/17 Note intriguing coincidences: −9 −10 2 aPioneer ≈ aHubble ≈ aMOND ≈ aΛ ≈ 10 − 10 m/s | {z } | {z } | {z } |{z} Solar system Galaxies Galaxies Supernovae

Prize question: success or failure of ‘Dark Hypotheses’?

? ... and in case of failure: what are alternative explanations?!

Experimental Introduction Gravitational Anomalies, Summary Experimental anomalies discovered in recent decade:

I Dark Energy (73% of our Universe!) I Dark Matter (23% of our Universe!) I Pioneer anomaly (is it for real?) I Fly-by anomaly, Increase of astronomical units, ... (fake or real?)

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 9/17 Prize question: success or failure of ‘Dark Hypotheses’?

? ... and in case of failure: what are alternative explanations?!

Experimental Introduction Gravitational Anomalies, Summary Experimental anomalies discovered in recent decade:

I Dark Energy (73% of our Universe!) I Dark Matter (23% of our Universe!) I Pioneer anomaly (is it for real?) I Fly-by anomaly, Increase of astronomical units, ... (fake or real?) Note intriguing coincidences: −9 −10 2 aPioneer ≈ aHubble ≈ aMOND ≈ aΛ ≈ 10 − 10 m/s | {z } | {z } | {z } |{z} Solar system Galaxies Galaxies Supernovae

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 9/17 ? ... and in case of failure: what are alternative explanations?!

Experimental Introduction Gravitational Anomalies, Summary Experimental anomalies discovered in recent decade:

Prize question: success or failure of ‘Dark Hypotheses’?

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 9/17 Experimental Introduction Gravitational Anomalies, Summary Experimental anomalies discovered in recent decade:

Prize question: success or failure of ‘Dark Hypotheses’?

? ... and in case of failure: what are alternative explanations?!

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 9/17 Several Dark Energy explanations seem viable: I Simplest explanation: cosmological constant (with ensuing problem) I More complicated explanations: quintessence, scalar-tensor theories I Interesting approach: cosmic acceleration from non-linearities in General Relativity (see next talk by Herbert Balasin) Dark Matter Alternatives are at least as problematic as Dark Matter:

I Often in conﬂict with solar system precision tests... I ...or ad-hoc (like MOND) I What about explanations within General Relativity?

Focus on simple but signiﬁcant system, namely a Galaxy!

Theoretical Introduction Alternatives to Dark Physics

Main motivation: no independent detection of dark particles (yet)!

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 10/17 Dark Matter Alternatives are at least as problematic as Dark Matter:

I Often in conﬂict with solar system precision tests... I ...or ad-hoc (like MOND) I What about explanations within General Relativity?

Focus on simple but signiﬁcant system, namely a Galaxy!

Theoretical Introduction Alternatives to Dark Physics

Main motivation: no independent detection of dark particles (yet)!

Several Dark Energy explanations seem viable: I Simplest explanation: cosmological constant (with ensuing problem) I More complicated explanations: quintessence, scalar-tensor theories I Interesting approach: cosmic acceleration from non-linearities in General Relativity (see next talk by Herbert Balasin)

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 10/17 Focus on simple but signiﬁcant system, namely a Galaxy!

Theoretical Introduction Alternatives to Dark Physics

Main motivation: no independent detection of dark particles (yet)!

I Often in conﬂict with solar system precision tests... I ...or ad-hoc (like MOND) I What about explanations within General Relativity?

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 10/17 Theoretical Introduction Alternatives to Dark Physics

Main motivation: no independent detection of dark particles (yet)!

I Often in conﬂict with solar system precision tests... I ...or ad-hoc (like MOND) I What about explanations within General Relativity?

Focus on simple but signiﬁcant system, namely a Galaxy!

D. Grumiller — Dark Matter and Alternatives PART I: Introduction 10/17 Outline

PART I: Introduction Historic Introduction Experimental Introduction Theoretical Introduction

Galactic Rotation Curves Status quo Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems

PART II: H. Balasin “Nonlinear eﬀects in gravitationally bound systems” PART III: F. Preis “Rotational Velocity in General Relativity”

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 11/17 Experimental data A typical galactic rotation curve

I Curve A: Newtonian prediction

I Curve B: Observed velocity proﬁle

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 12/17 Exciting prospect for near future:

Dark Matter might be discovered right now at LHC!

Dark Matter

I Postulate existence of Dark Matter I Fit Dark Matter density as to “explain” rotation curves Note: other hints for Dark Matter, e.g. gravitational lensing!

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 13/17 Dark Matter

I Postulate existence of Dark Matter I Fit Dark Matter density as to “explain” rotation curves Note: other hints for Dark Matter, e.g. gravitational lensing! Exciting prospect for near future:

Dark Matter might be discovered right now at LHC!

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 13/17 I Do we have the correct theory of gravity?

I Are we applying it correctly? Possible answers:

I Regarding 1: e.g. MOND, IR modiﬁcations of GR, Yukawa-type corrections, ...

I Regarding 2: Newtonian limit justiﬁed? The second question is relevant in presence and absence of Dark Matter! Answer for simple toy model:

About 30% reduction of Dark Matter by General Relativistic eﬀects!

H. Balasin and D. Grumiller, Int. J. Mod. Phys. 17 (2008) 475–488.

Main Issues of Alternatives to Dark Matter Two important questions:

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 14/17 I Are we applying it correctly? Possible answers:

I Regarding 1: e.g. MOND, IR modiﬁcations of GR, Yukawa-type corrections, ...

I Regarding 2: Newtonian limit justiﬁed? The second question is relevant in presence and absence of Dark Matter! Answer for simple toy model:

About 30% reduction of Dark Matter by General Relativistic eﬀects!

H. Balasin and D. Grumiller, Int. J. Mod. Phys. 17 (2008) 475–488.

Main Issues of Alternatives to Dark Matter Two important questions:

I Do we have the correct theory of gravity?

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 14/17 Possible answers:

I Regarding 1: e.g. MOND, IR modiﬁcations of GR, Yukawa-type corrections, ...

I Regarding 2: Newtonian limit justiﬁed? The second question is relevant in presence and absence of Dark Matter! Answer for simple toy model:

About 30% reduction of Dark Matter by General Relativistic eﬀects!

H. Balasin and D. Grumiller, Int. J. Mod. Phys. 17 (2008) 475–488.

Main Issues of Alternatives to Dark Matter Two important questions:

I Do we have the correct theory of gravity?

I Are we applying it correctly?

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 14/17 Answer for simple toy model:

About 30% reduction of Dark Matter by General Relativistic eﬀects!

H. Balasin and D. Grumiller, Int. J. Mod. Phys. 17 (2008) 475–488.

Main Issues of Alternatives to Dark Matter Two important questions:

I Do we have the correct theory of gravity?

I Are we applying it correctly? Possible answers:

I Regarding 1: e.g. MOND, IR modiﬁcations of GR, Yukawa-type corrections, ...

I Regarding 2: Newtonian limit justiﬁed? The second question is relevant in presence and absence of Dark Matter!

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 14/17 Main Issues of Alternatives to Dark Matter Two important questions:

I Do we have the correct theory of gravity?

I Are we applying it correctly? Possible answers:

I Regarding 1: e.g. MOND, IR modiﬁcations of GR, Yukawa-type corrections, ...

I Regarding 2: Newtonian limit justiﬁed? The second question is relevant in presence and absence of Dark Matter! Answer for simple toy model:

About 30% reduction of Dark Matter by General Relativistic eﬀects!

H. Balasin and D. Grumiller, Int. J. Mod. Phys. 17 (2008) 475–488.

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 14/17 I Gravity is weak in Galaxy (besides the centre): rS/r 1

I Thus, locally Newton approximation valid at each point!

I However, Galaxy is not a point source but an extended source

I Conceivable that Newton approximation breaks down at large scales

I In fact, this is what happens in toy model considered previously

I Consequence of exact General Relativist calculation: reduction (but not elimination) of Dark Matter

I Question: artifact of toy model or genuine eﬀect?

Go beyond toy model by dropping some simplifying assumptions =⇒ Main point of our project!

Technical details: see project proposal!

Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems Why can there be an eﬀect at all?

−3 I Velocity of stars in Galaxy is small: v/c . 10

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 15/17 I Thus, locally Newton approximation valid at each point!

I However, Galaxy is not a point source but an extended source

I Conceivable that Newton approximation breaks down at large scales

I In fact, this is what happens in toy model considered previously

I Consequence of exact General Relativist calculation: reduction (but not elimination) of Dark Matter

I Question: artifact of toy model or genuine eﬀect?

Go beyond toy model by dropping some simplifying assumptions =⇒ Main point of our project!

Technical details: see project proposal!

Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems Why can there be an eﬀect at all?

−3 I Velocity of stars in Galaxy is small: v/c . 10 I Gravity is weak in Galaxy (besides the centre): rS/r 1

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 15/17 I However, Galaxy is not a point source but an extended source

I Conceivable that Newton approximation breaks down at large scales

I In fact, this is what happens in toy model considered previously

I Consequence of exact General Relativist calculation: reduction (but not elimination) of Dark Matter

I Question: artifact of toy model or genuine eﬀect?

Go beyond toy model by dropping some simplifying assumptions =⇒ Main point of our project!

Technical details: see project proposal!

Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems Why can there be an eﬀect at all?

−3 I Velocity of stars in Galaxy is small: v/c . 10 I Gravity is weak in Galaxy (besides the centre): rS/r 1

I Thus, locally Newton approximation valid at each point!

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 15/17 I Conceivable that Newton approximation breaks down at large scales

I In fact, this is what happens in toy model considered previously

I Consequence of exact General Relativist calculation: reduction (but not elimination) of Dark Matter

I Question: artifact of toy model or genuine eﬀect?

Go beyond toy model by dropping some simplifying assumptions =⇒ Main point of our project!

Technical details: see project proposal!

Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems Why can there be an eﬀect at all?

−3 I Velocity of stars in Galaxy is small: v/c . 10 I Gravity is weak in Galaxy (besides the centre): rS/r 1

I Thus, locally Newton approximation valid at each point!

I However, Galaxy is not a point source but an extended source

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 15/17 I In fact, this is what happens in toy model considered previously

I Consequence of exact General Relativist calculation: reduction (but not elimination) of Dark Matter

I Question: artifact of toy model or genuine eﬀect?

Go beyond toy model by dropping some simplifying assumptions =⇒ Main point of our project!

Technical details: see project proposal!

Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems Why can there be an eﬀect at all?

−3 I Velocity of stars in Galaxy is small: v/c . 10 I Gravity is weak in Galaxy (besides the centre): rS/r 1

I Thus, locally Newton approximation valid at each point!

I However, Galaxy is not a point source but an extended source

I Conceivable that Newton approximation breaks down at large scales

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 15/17 I Consequence of exact General Relativist calculation: reduction (but not elimination) of Dark Matter

I Question: artifact of toy model or genuine eﬀect?

Go beyond toy model by dropping some simplifying assumptions =⇒ Main point of our project!

Technical details: see project proposal!

Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems Why can there be an eﬀect at all?

−3 I Velocity of stars in Galaxy is small: v/c . 10 I Gravity is weak in Galaxy (besides the centre): rS/r 1

I Thus, locally Newton approximation valid at each point!

I However, Galaxy is not a point source but an extended source

I Conceivable that Newton approximation breaks down at large scales

I In fact, this is what happens in toy model considered previously

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 15/17 I Question: artifact of toy model or genuine eﬀect?

Go beyond toy model by dropping some simplifying assumptions =⇒ Main point of our project!

Technical details: see project proposal!

Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems Why can there be an eﬀect at all?

−3 I Velocity of stars in Galaxy is small: v/c . 10 I Gravity is weak in Galaxy (besides the centre): rS/r 1

I Thus, locally Newton approximation valid at each point!

I However, Galaxy is not a point source but an extended source

I Conceivable that Newton approximation breaks down at large scales

I In fact, this is what happens in toy model considered previously

I Consequence of exact General Relativist calculation: reduction (but not elimination) of Dark Matter

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 15/17 Go beyond toy model by dropping some simplifying assumptions =⇒ Main point of our project!

Technical details: see project proposal!

Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems Why can there be an eﬀect at all?

−3 I Velocity of stars in Galaxy is small: v/c . 10 I Gravity is weak in Galaxy (besides the centre): rS/r 1

I Thus, locally Newton approximation valid at each point!

I However, Galaxy is not a point source but an extended source

I Conceivable that Newton approximation breaks down at large scales

I In fact, this is what happens in toy model considered previously

I Consequence of exact General Relativist calculation: reduction (but not elimination) of Dark Matter

I Question: artifact of toy model or genuine eﬀect?

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 15/17 Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems Why can there be an eﬀect at all?

−3 I Velocity of stars in Galaxy is small: v/c . 10 I Gravity is weak in Galaxy (besides the centre): rS/r 1

I Thus, locally Newton approximation valid at each point!

I However, Galaxy is not a point source but an extended source

I Conceivable that Newton approximation breaks down at large scales

I In fact, this is what happens in toy model considered previously

I Consequence of exact General Relativist calculation: reduction (but not elimination) of Dark Matter

I Question: artifact of toy model or genuine eﬀect?

Go beyond toy model by dropping some simplifying assumptions =⇒ Main point of our project!

Technical details: see project proposal!

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 15/17 I Problem: Einstein-equations prohibitively diﬃcult to solve! I Solution: Make reasonable simplifying assumptions

Simplifying assumptions: axisymmetry and stationarity!

Technical details of axisymmetric stationary geometries: see fact sheet! Spin-oﬀ: same techniques useful for accretion disks (collaboration with Bruno Coppi and Paola Rebusco at MIT)

Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems Outlook to next two presentations: How to model a Galaxy Equations to solve (Einstein-equations): 1 Rab − gabR = κ T ab 2 Perfect ﬂuid energy-momentum tensor: ab a b ab a b T = ρm u u + P g + u u

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 16/17 I Solution: Make reasonable simplifying assumptions

Simplifying assumptions: axisymmetry and stationarity!

Technical details of axisymmetric stationary geometries: see fact sheet! Spin-oﬀ: same techniques useful for accretion disks (collaboration with Bruno Coppi and Paola Rebusco at MIT)

I Problem: Einstein-equations prohibitively diﬃcult to solve!

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 16/17 Simplifying assumptions: axisymmetry and stationarity!

Technical details of axisymmetric stationary geometries: see fact sheet! Spin-oﬀ: same techniques useful for accretion disks (collaboration with Bruno Coppi and Paola Rebusco at MIT)

I Problem: Einstein-equations prohibitively diﬃcult to solve! I Solution: Make reasonable simplifying assumptions

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 16/17 Spin-oﬀ: same techniques useful for accretion disks (collaboration with Bruno Coppi and Paola Rebusco at MIT)

I Problem: Einstein-equations prohibitively diﬃcult to solve! I Solution: Make reasonable simplifying assumptions

Simplifying assumptions: axisymmetry and stationarity!

Technical details of axisymmetric stationary geometries: see fact sheet!

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 16/17 Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems Outlook to next two presentations: How to model a Galaxy Equations to solve (Einstein-equations): 1 Rab − gabR = κ T ab 2 Perfect ﬂuid energy-momentum tensor: ab a b ab a b T = ρm u u + P g + u u

I Problem: Einstein-equations prohibitively diﬃcult to solve! I Solution: Make reasonable simplifying assumptions

Simplifying assumptions: axisymmetry and stationarity!

Technical details of axisymmetric stationary geometries: see fact sheet! Spin-oﬀ: same techniques useful for accretion disks (collaboration with Bruno Coppi and Paola Rebusco at MIT)

D. Grumiller — Dark Matter and Alternatives Galactic Rotation Curves 16/17 Outline

PART I: Introduction Historic Introduction Experimental Introduction Theoretical Introduction

Galactic Rotation Curves Status quo Non-perturbative Eﬀects of Rotation in Gravitationally Bound Systems

PART II: H. Balasin “Nonlinear eﬀects in gravitationally bound systems” PART III: F. Preis “Rotational Velocity in General Relativity”

D. Grumiller — Dark Matter and Alternatives PART II: H. Balasin “Nonlinear eﬀects in gravitationally bound systems” PART III: F. Preis “Rotational Velocity in General Relativity” 17/17