Kent Yagi BLACK HOLE SOLUTION AND BINARY GRAVITATIONAL WAVES IN DYNAMICAL CHERN-SIMONS GRAVITY. (Montana State University)

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1 BLACK HOLE SOLUTION AND BINARY GRAVITATIONAL WAVES IN DYNAMICAL CHERN-SIMONS GRAVITY University of Tokyo November 13 th 2012 Kent Yagi (Montana State University) Collaborators: Nicolas Yunes (Montana State Univ.) Takahiro Tanaka (YITP)

2 Contents 1 Introduction 2 Black Hole Solutions 3 Gravitational Waves from BH Binaries 4 Summary & Future Work

3 Contents 1 Introduction 2 Black Hole Solutions 3 Gravitational Waves from BH Binaries 4 Summary & Future Work

4 Probing alternative theories of gravity using compact binaries Why modifications of gravity? (I) Problems within GR can be naturally solved. (II) Classical gravitational theory as a low-energy effective theory of a more fundamental theory e.g. superstring theory Chern-Simons, Gauss-Bonnet, Scalar-tensor theories

5 Testing GR (I) Weak field, non-dynamical regime: Solar System Binary Pulsar (II) Strong field, dynamical regime: Gravitational Waves

6 Dynamical Chern-Simons Gravity -Standard Model -Superstring Theory -Loop Quantum Gravity -Inflation

7 Action: Dynamical Chern-Simons Gravity -Standard Model -Superstring Theory -Loop Quantum Gravity -Inflation

8 Action: Dynamical Chern-Simons Gravity -Standard Model -Superstring Theory -Loop Quantum Gravity -Inflation Field Eqs.:

9 Action: Dynamical Chern-Simons Gravity -Standard Model -Superstring Theory -Loop Quantum Gravity -Inflation Field Eqs.: Characteristic Length Scale:

10 -Standard Model -Superstring Theory Action: Dynamical Chern-Simons Gravity -Loop Quantum Gravity -Inflation Field Eqs.: Characteristic Length Scale: Small coupling approximation Dimensionless coupling constant: For simplicity, we set

11 Corrections to GWs from BH Binaries (I) Dissipative Scalar & Gravitational Radiation Modifies the orbital evolution (II) Conservative Modified BH Solution Modifies the binding energy Modifies the binary orbit

12 Dissipative Corrections in DCS Gravity Non-Spinning BH Pert. PN 7PN effect For the spinning case, the correction is 2PN! Now, we need to compute the conservative one. [KY+ (2012)]

13 Contents 1 Introduction 2 Black Hole Solutions 3 Gravitational Waves from BH Binaries 4 Summary & Future Work

14 (I) Non-Spinning Spherical Symmetry No CS correction Schwarzschild BH

15 (I) Non-Spinning Spherical Symmetry GPB (II) Spinning No CS correction Schwarzschild BH -Exact Solution unknown. -Linear order in spin [Yunes & Pretorius (2009), Konno et al. (2009)] frame-dragging effect Gravity Probe B [Ali-Haimoud & Chen (2011)]

16 BH Solution at Quadratic Order in Spin Metric Perturbation: GR CS

17 BH Solution at Quadratic Order in Spin Metric Perturbation: Expansion in spin: GR CS

18 BH Solution at Quadratic Order in Spin Metric Perturbation: Expansion in spin: GR CS

19 BH Solution at Quadratic Order in Spin Metric Perturbation: Expansion in spin: GR CS

20 BH Solution at Quadratic Order in Spin Metric Perturbation: Expansion in spin: GR CS Yunes & Pretorius, Konno et al.

21 BH Solution at Quadratic Order in Spin Metric Perturbation: Expansion in spin: GR CS v Yunes & Pretorius, Konno et al. New!!

22 BH Solution at Quadratic Order in Spin Metric Perturbation: Expansion in spin: GR CS v Yunes & Pretorius, Konno et al. New!! Field Eqs.: at order (2,2)

23 BH Solution at Quadratic Order in Spin Metric Perturbation: Expansion in spin: GR CS v Yunes & Pretorius, Konno et al. New!! Field Eqs.: at order (2,2) Known functions

24 BH Solution at Quadratic Order in Spin Metric Perturbation: Expansion in spin: GR CS v Yunes & Pretorius, Konno et al. New!! Field Eqs.: at order (2,2) v Perturbation under Schw. BH Known functions

25 BH Solution at Quadratic Order in Spin Metric Perturbation: Expansion in spin: GR CS v Yunes & Pretorius, Konno et al. New!! Field Eqs.: at order (2,2) v Perturbation under Schw. BH Known functions Spherical harmonic decomposition decouples

26 The New Metric [KY+ (2012)]

27 Contents 1 Introduction 2 Black Hole Solutions 3 Gravitational Waves from BH Binaries 4 Summary & Future Work

28 GWs from BH Binaries in CS Gravity parameterized post-einsteinian waveform: Yunes & Pretorius (2009)

29 GWs from BH Binaries in CS Gravity parameterized post-einsteinian waveform: Yunes & Pretorius (2009) CS Gravity: 2PN correction Amplitude 加速膨張による補正 GR CS Binary GW time

30 GW DETECTORS amplitude SMBH IMBH stellar-mass BH LISA DECIGO/BBO adv. LIGO KAGRA ET

31 Results: Adv. LIGO, KAGRA Constraints on Spins are known a priori Colored Region: total mass [KY+ (2012)]

32 Results: Adv. LIGO, KAGRA Constraints on Spins are known a priori Colored Region: total mass [KY+ (2012)]

33 Results: Adv. LIGO, KAGRA Constraints on Spins are known a priori Colored Region: The bound roughly corresponds to the BH horizon size. total mass [KY+ (2012)]

34 Results: Adv. LIGO, KAGRA Constraints on Spins are known a priori Colored Region: The bound roughly corresponds to the BH horizon size. Solar system: total mass [KY+ (2012)]

35 Results: Adv. LIGO, KAGRA Constraints on Spins are known a priori Colored Region: The bound roughly corresponds to the BH horizon size. Solar system: total mass [KY+ (2012)] 7 orders of magnitude stronger constraint than the solar system bound!!

36 Results: Other Detectors spin (anti-)aligned binaries (Spins are included into parameters.)

37 Contents 1 Introduction 2 Black Hole Solutions 3 Gravitational Waves from BH Binaries 4 Summary & Future Work

38 -New BH Solution to quadratic order in spin 2PN Conservative Correction -PN Scheme 2PN Dissipative Correction First self-consistent BH Binary gravitational waveforms 2 nd generation ground-based interferometers 7 orders of magnitude stronger constraint than the solar system bound!! Future Work - Precessing BH binaries - Bayesian analysis, more realistic detector noises - Modeling NSs in dynamical CS gravity Current constraints from double binary pulsar obs.