The Exterior Spacetime of Relativistic Stars in Quadratic Gravity - PowerPoint PPT Presentation

The Exterior Spacetime of Relativistic Stars in Quadratic Gravity Alexander Saffer eXtreme Gravity Institute Montana State University Advisor: Nicolas Yunes October 10, 2018

Outlook Motivation Why Quadratic Gravity Neutron Stars Finding the Metric U. of Melbourne - 10/10/2018 Alexander Saffer 1

Motivation Brief History of GR 1905 - Special Relativity Equivalence of observation Speed of light is constant Time dilation/length contraction 1915 - General Relativity Curvature of space-time is related to energy present Curvature representative of gravity Figure: Original 1915 Paper U. of Melbourne - 10/10/2018 Alexander Saffer 2

Motivation Passed Tests What’s wrong with GR? Perihelion Precession of Mercury Figure: Mercury Orbit U. of Melbourne - 10/10/2018 Alexander Saffer 3

Motivation Passed Tests What’s wrong with GR? Perihelion Precession of Mercury Light Bending Figure: A. Eddington U. of Melbourne - 10/10/2018 Alexander Saffer 3

Motivation Passed Tests What’s wrong with GR? Perihelion Precession of Mercury Light Bending Gravitational Redshift Figure: Gravitational Redshift (wikipedia) U. of Melbourne - 10/10/2018 Alexander Saffer 3

Motivation Passed Tests What’s wrong with GR? Perihelion Precession of Mercury Light Bending Gravitational Redshift Shapiro Delay Figure: Shapiro Delay (Brian Koberlein) U. of Melbourne - 10/10/2018 Alexander Saffer 3

Motivation Passed Tests What’s wrong with GR? Perihelion Precession of Mercury Light Bending Gravitational Redshift Shapiro Delay Frame Dragging Figure: Gravity Probe B U. of Melbourne - 10/10/2018 Alexander Saffer 3

Motivation Passed Tests What’s wrong with GR? Perihelion Precession of Mercury Light Bending Gravitational Redshift Shapiro Delay Frame Dragging Geodetic Effect Figure: Gravity Probe B U. of Melbourne - 10/10/2018 Alexander Saffer 3

Motivation Passed Tests What’s wrong with GR? Perihelion Precession of Mercury Light Bending Gravitational Redshift Shapiro Delay Frame Dragging Geodetic Effect Binary Pulsars Figure: Hulse-Taylor Binary U. of Melbourne - 10/10/2018 Alexander Saffer 3

Motivation Passed Tests What’s wrong with GR? Perihelion Precession of Mercury Light Bending Gravitational Redshift Shapiro Delay Frame Dragging Geodetic Effect Binary Pulsars Gravitational Waves Figure: (LIGO) Gravitational Waves U. of Melbourne - 10/10/2018 Alexander Saffer 3

Motivation When asked how he would have felt if his theory would fail Then I would feel sorry for the dear Lord. The theory is correct anyway. - Albert Einstein (1919) U. of Melbourne - 10/10/2018 Alexander Saffer 4

Motivation Why Test GR? Quantum Mechanics GR is a classical theory Not quantized Cannot reconcile with other forces Cosmology Inflation Dark Matter Dark Energy More testing in strong-field Solar System tests passed Probe area near compact objects U. of Melbourne - 10/10/2018 Alexander Saffer 5

Why Quadratic Gravity Quadratic Gravity Motivation Some quantum gravity theories (string theory, loop quantum gravity) induce higher order curvature terms naturally GR may be corrected at low energy scales to gain higher order curvature terms Curvature squared terms R 2 R ab R ab R abcd R abcd ∗ R abcd R abcd U. of Melbourne - 10/10/2018 Alexander Saffer 6

Why Quadratic Gravity Einstein-dilaton-Gauss-Bonnet* (EdGB) Action � √− g � κ R + α φ R GB − 1 � 2 ( ∇ a φ ) ( ∇ a φ ) − V ( φ ) S = + S m with κ = ( 16 π G ) − 1 R GB = R 2 − 4 R ab R ab + R abcd R abcd α/ L 2 ≪ 1 � � Small corrections to GR Field Equations ab + T φ κ G ab + T GB ab = T m ab � φ = − α R GB U. of Melbourne - 10/10/2018 Alexander Saffer 7

Neutron Stars Introduction to Neutron Stars Formed from collapse of large star Mass ∼ 1.4 - 2 M ⊙ Radius ∼ 10 km U. of Melbourne - 10/10/2018 Alexander Saffer 8

Neutron Stars Introduction to Neutron Stars Huge densities ∼ 10 15 [ g / cm 3 ] Huge surface gravity ∼ 10 12 [ m / s 2 ] Figure: Corvin Zahn, Institut für Physik, Universität Hildesheim, Tempolimit Lichtgeschwindigkeit (M=1, R=4) U. of Melbourne - 10/10/2018 Alexander Saffer 9

Neutron Stars Introduction to Neutron Stars Huge magnetic fields 10 4 − 10 11 [ T ] Rotating NS → Pulsars U. of Melbourne - 10/10/2018 Alexander Saffer 10

Neutron Stars Figure: NASA U. of Melbourne - 10/10/2018 Alexander Saffer 11

Neutron Stars Figure: J. Poutanen - arxiv:0809.2400[astro-ph] U. of Melbourne - 10/10/2018 Alexander Saffer 12

Neutron Stars Scalar-Tensor Theory Figure: H.O. Silva and N. Yunes - arxiv:1808.04391[gr-qc] U. of Melbourne - 10/10/2018 Alexander Saffer 13

Finding the Metric What do we want Smooth Continuous Asymptotically flat Not singular U. of Melbourne - 10/10/2018 Alexander Saffer 14

Finding the Metric Ansatz Begin with the assumption ds 2 = − e 2 τ dt 2 + e 2 σ dr 2 + r 2 d Ω 2 Assume our expansions τ = τ 0 + α 2 τ 2 σ = σ 0 + α 2 σ 2 φ = φ 0 + α φ 1 Solve order-by-order U. of Melbourne - 10/10/2018 Alexander Saffer 15

Finding the Metric � α 0 � Exterior O Birkhoff’s Theorem 1 − a � � e 2 τ 0 = r 1 − a � − 1 � e 2 σ 0 = r ...that was easy (too easy) U. of Melbourne - 10/10/2018 Alexander Saffer 16

Finding the Metric � α 0 � Interior O Assume perfect fluid m = ( ρ + p ) u a u b + p g ab T ab u a u a = − 1 F.E. lead to Tolman-Oppenheimer-Volkoff equations ∂ r m = 4 πρ r 2 ∂ r τ 0 = 4 π pr 3 + m r ( r − 2 m ) 4 π pr 3 + m � � ( ρ + p ) ∂ r p = − r ( r − 2 m ) U. of Melbourne - 10/10/2018 Alexander Saffer 17

Finding the Metric � α 0 � Interior O Mass-Radius Curves Yes, a = 2 m U. of Melbourne - 10/10/2018 Alexander Saffer 18

Finding the Metric � α 0 � Interior O g tt Metric Solution U. of Melbourne - 10/10/2018 Alexander Saffer 19

Finding the Metric � α 0 � Interior O g tt Metric Solution U. of Melbourne - 10/10/2018 Alexander Saffer 20

Finding the Metric � α 2 � O Terms U. of Melbourne - 10/10/2018 Alexander Saffer 21

Finding the Metric Finally What? Finding the metric outside of a neutron star in modified gravity. Specifically, we are using EdGB, which can be shown as an extension of string theory. Why? To develop a model which can be tested with observations of NS pulse profiles. In an effort to place constraints on the theory. How? By building the analytic metric using perturbation theory and solving the field equations order by order. U. of Melbourne - 10/10/2018 Alexander Saffer 22

Finding the Metric Thank You Questions? U. of Melbourne - 10/10/2018 Alexander Saffer 23