Prologue String Theory Precision counting of microstates Black Hole Hair Analysis of the BMPV BH Entropy Analysis of the 4D BH Entropy Hair modes in Supergravity Regularity of Hair Modes Conclusion Shaving the Black Hole Yogesh K. Srivastava Work with Dileep Jatkar and Ashoke Sen KEK 25/11/2009 Yogesh K. Srivastava Work with Dileep Jatkar and Ashoke Sen Shaving the Black Hole
Prologue String Theory Precision counting of microstates Black Hole Hair Analysis of the BMPV BH Entropy Analysis of the 4D BH Entropy Hair modes in Supergravity Regularity of Hair Modes Conclusion Outline Prologue 1 Introduction String Theory 2 Introduction Black Holes in String theory Precision counting of microstates 3 Black Hole Hair 4 Analysis of the BMPV BH Entropy 5 Microscopic Description Macroscopic Description Hair Removal Analysis of the 4D BH Entropy 6 Microscopic Description Macroscopic description Hair Removal Hair modes in Supergravity 7 BMPV Black Hole Hair Fermionic Deformations Deformations of 4-dimensional black holes Regularity of Hair Modes 8 Conclusion 9 Yogesh K. Srivastava Work with Dileep Jatkar and Ashoke Sen Shaving the Black Hole
Prologue String Theory Precision counting of microstates Black Hole Hair Analysis of the BMPV BH Entropy Introduction Analysis of the 4D BH Entropy Hair modes in Supergravity Regularity of Hair Modes Conclusion Outline Prologue 1 Introduction String Theory 2 Introduction Black Holes in String theory Precision counting of microstates 3 Black Hole Hair 4 Analysis of the BMPV BH Entropy 5 Microscopic Description Macroscopic Description Hair Removal Analysis of the 4D BH Entropy 6 Microscopic Description Macroscopic description Hair Removal Hair modes in Supergravity 7 BMPV Black Hole Hair Fermionic Deformations Deformations of 4-dimensional black holes Regularity of Hair Modes 8 Conclusion 9 Yogesh K. Srivastava Work with Dileep Jatkar and Ashoke Sen Shaving the Black Hole
Prologue String Theory Precision counting of microstates Black Hole Hair Analysis of the BMPV BH Entropy Introduction Analysis of the 4D BH Entropy Hair modes in Supergravity Regularity of Hair Modes Conclusion Clots of gravity One of the most exciting predictions of Einstein’s General Relativity(GR) is that there exist Black Holes: objects whose gravitational fields are so strong that no body or signal can break free and escape. Occupy special position in observational astrophysics, theoretical efforts at unification of forces etc. Reveal profound relationships between gravitation, quantum theory and thermodynamics. Many fundamental ideas like Holographic principle, string dualities etc are related to the study of black holes. Black Holes provide a very useful context where quantum gravitational effects are calculable and highly precise tests are possible. They lead to non-trivial tests of nonperturbative consistency of string theory as a theory of quantum gravity. Black Holes are the extreme examples of dynamical nature of space-time( expressed by metric tensor) in General Relativity. Yogesh K. Srivastava Work with Dileep Jatkar and Ashoke Sen Shaving the Black Hole
Prologue String Theory Precision counting of microstates Black Hole Hair Analysis of the BMPV BH Entropy Introduction Analysis of the 4D BH Entropy Hair modes in Supergravity Regularity of Hair Modes Conclusion Particle� Future � Particle� Light ray� Particle� of E� Time� E� Space� Light � rays� Time� Past� Space� of E� Figure 3� Figure 2� Yogesh K. Srivastava Work with Dileep Jatkar and Ashoke Sen Shaving the Black Hole
Prologue String Theory Precision counting of microstates Black Hole Hair Analysis of the BMPV BH Entropy Introduction Analysis of the 4D BH Entropy Hair modes in Supergravity Regularity of Hair Modes Conclusion Properties Light Imprisoned Black Holes can occur as end products of complete gravitational collapse. Theoretically, they are solutions to equations of general relativity. Black Holes have a singularity, covered by an imaginary surface, Event Horizon which serves as a causal boundary. Schwarzschild Black Holes : ds 2 = (1 − r h r ) dt 2 + (1 − r h r ) − 1 dr 2 + r 2 d Ω 2 2 Spherically symmetric,non-rotating. Radius of event horizon r h = 2 GM / c 2 . For an object to be black hole, r h ≫ λ c where λ c is the compton wavelength. Surface gravity κ is the force required by a faraway observer to hold a unit mass c 4 at the horizon. For Schwarzschild BH, κ = 4 GM . Yogesh K. Srivastava Work with Dileep Jatkar and Ashoke Sen Shaving the Black Hole
Prologue String Theory Precision counting of microstates Black Hole Hair Analysis of the BMPV BH Entropy Introduction Analysis of the 4D BH Entropy Hair modes in Supergravity Regularity of Hair Modes Conclusion � distant� astronomer� r = 0� singularity� R� 3� event� horizon� r = 2M� light� cones� R� 2� outgoing� light� rays� R� 1� E� 4� E� 3� E� 2� Time� ingoing� E� 1� light� rays� Space� surface� star� of the� Figure 4� Yogesh K. Srivastava Work with Dileep Jatkar and Ashoke Sen Shaving the Black Hole
Prologue String Theory Precision counting of microstates Black Hole Hair Analysis of the BMPV BH Entropy Introduction Analysis of the 4D BH Entropy Hair modes in Supergravity Regularity of Hair Modes Conclusion Black Hole thermodynamics Classical black holes satisfy several theorems which are tantalizingly like laws of thermodynamics Laws of Thermodynamics Zeroth Law: T constant throughout body in thermal equilibrium First Law: dE = TdS + workterms Second Law: Change in Entropy δ S ≥ 0 in any process. Third Law: Impossible to achieve T = 0 in physical processes Laws of Black Hole Mechanics Zeroth Law:Surface gravity κ is constant over the horizon of a stationary black hole. κ First Law: dM = 8 π G dA + ω h dJ + Φ e dQ Second Law: Change in the area of the event horizon δ A ≥ 0 always increases in any classical process. Third Law:It is impossible to achieve κ = 0 in finite number of steps. Yogesh K. Srivastava Work with Dileep Jatkar and Ashoke Sen Shaving the Black Hole
Prologue String Theory Precision counting of microstates Black Hole Hair Analysis of the BMPV BH Entropy Introduction Analysis of the 4D BH Entropy Hair modes in Supergravity Regularity of Hair Modes Conclusion Area Law Collision of two� Growth of a� black holes� black hole� A� t� 1� > A + A� 1� 2� 2� Formation of a� black hole� A� A� t� 1� 2� 1� time� space� Formation� Yogesh K. Srivastava Work with Dileep Jatkar and Ashoke Sen Shaving the Black Hole Figure 11�
Prologue String Theory Precision counting of microstates Black Hole Hair Analysis of the BMPV BH Entropy Introduction Analysis of the 4D BH Entropy Hair modes in Supergravity Regularity of Hair Modes Conclusion Semi-classical Black Holes Black Holes and Second Law of Thermodynamics One can violate second law of thermodynamics in observable universe by throwing stuff into black holes. Based on analogy of black holes with laws of thermodynamics, Beckenstein proposed to save second law by assigning black hole an entropy proportional to area. Hawking coupled quantum matter to a classical black hole and showed that they h κ emit black body radiation at a temperature T = 2 π c . For Schwarzschild BH, T ≈ 6 × 10 − 8 ( M sun / M ) K Given the black hole temperature, first law of BH mechanics assigns an entropy S BH = Ac 3 4 hG to black hole. S total = S matter + S BH obeys the second law. In conventional statistical mechanics, entropy of a system has a microscopic explanation. S = lnd micro . Here d micro is the number of (quantum) microstates available to the system for a given set of macroscopic charges like energy, total electric charge etc. Huge entropy of the black hole implies that it should have large number of microstates. For M = M sun , no. of d.o.f is ∼ 10 10 78 ! Yogesh K. Srivastava Work with Dileep Jatkar and Ashoke Sen Shaving the Black Hole
Prologue String Theory Precision counting of microstates Black Hole Hair Introduction Analysis of the BMPV BH Entropy Black Holes in String theory Analysis of the 4D BH Entropy Hair modes in Supergravity Regularity of Hair Modes Conclusion Outline Prologue 1 Introduction String Theory 2 Introduction Black Holes in String theory Precision counting of microstates 3 Black Hole Hair 4 Analysis of the BMPV BH Entropy 5 Microscopic Description Macroscopic Description Hair Removal Analysis of the 4D BH Entropy 6 Microscopic Description Macroscopic description Hair Removal Hair modes in Supergravity 7 BMPV Black Hole Hair Fermionic Deformations Deformations of 4-dimensional black holes Regularity of Hair Modes 8 Conclusion 9 Yogesh K. Srivastava Work with Dileep Jatkar and Ashoke Sen Shaving the Black Hole
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