Fundamental Physics with Black Holes
In this chapter we discuss how quantum gravitational and quantum mechanical effects can affect black holes. In particular, we discuss how Planckian quantum black holes enable us to probe quantum gravitational physics either directly if the Planck scale is
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Fundamental Physics with Black Holes Xavier Calmet
Abstract In this chapter we discuss how quantum gravitational and quantum mechanical effects can affect black holes. In particular, we discuss how Planckian quantum black holes enable us to probe quantum gravitational physics either directly if the Planck scale is low enough or indirectly if we integrate out quantum black holes from our low energy effective action. We discuss how quantum black holes can resolve the information paradox of black holes and explain that quantum black holes lead to one of the few hard facts we have so far about quantum gravity, namely the existence of a minimal length in nature. Keywords Black holes · Quantum black holes · Tests of the Planck scale · General relativity · Effective field theory of quantum gravity · Planck length
1.1 Introduction Black holes are among the most fascinating objects in our universe. Their existence is now indisputable. Astrophysicists have observed very massive objects, which do not emit light. Obviously, these objects cannot be seen directly, but their gravitational effects on visible matter have clearly been established. The only reasonable explanation for these observations is that black holes do truly exist as predicted by Einstein’s theory of general relativity. From an astrophysicist point of view, black holes are regions of space-time where gravity is so strong that nothing, not even light, can escape from that region of space-time. Astrophysical black holes can have an accretion disk and sometimes a jet. A real black hole system is thus a rather complicated environment. In contrast, from a mathematical point of view, stationary black holes are very simple objects. They are vacuum solutions to Einsteins equations. The simplicity of black holes is reflected in the no-hair theorem [1] which states that black holes are uniquely defined in terms of just three parameters their mass, their electric charge and X. Calmet (B) Physics and Astronomy, University of Sussex, Falmer, Brighton, BN1 9QH, UK e-mail: [email protected] © Springer International Publishing Switzerland 2015 X. Calmet (ed.), Quantum Aspects of Black Holes, Fundamental Theories of Physics 178, DOI 10.1007/978-3-319-10852-0_1
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their angular momentum. How comes such simple objects can be so interesting? The answer lies in the fact that their physics merges three different branches of physics: general relativity, quantum mechanics and statistical physics. The first black hole solution was found by Schwarzschild only a couple of years after the publication of Einstein’s theory of general relativity [2]. The Schwarzschild metric is given by: 2MG 2 2 2MG −1 2 c dt + 1 − 2 dr + r 2 (dθ 2 + sin2 θ dϕ 2 ), (1.1) ds = − 1 − 2 c r c r
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where G is Newton’s constant, M is the mass of the black hole and c is the speed of light in vacuum and (r, θ, ϕ) are the usual spherical polar coordinates. The Kerr solution [3], which is relevant to astrophysical black holes was found much later in 1963. The Kerr solution represents a
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