1. Gravitational Physics: Quantum Gravity and Other Theoretical Aspects Luca BombelliTibor Torma Arif Caixia Gao Brian Mazur approaches to quantum gravity: causal sets, loop quantum gravity other projects: black-hole entropy, star clusters and star formation

2. what is quantum gravity? General relativity: Gravity is a consequence of the curvature of spacetime, some of whose components obey the equation curvature = 8  G (energy-momentum) ; as a consequence, spacetime geometry (the metric g  ) in part depends on matter, and in part it has its own wavelike dynamics. Is this the final word on gravity? Almost certainly not, because of quantum matter if nothing else. What about quantizing gravity itself? Ok, and we can perhaps guess what such a theory might tell us, but the first big question is, How? The most developed approaches are string theory and loop quantum gravity, but there are more radical ones. General relativity: Gravity is a consequence of the curvature of spacetime, some of whose components obey the equation curvature = 8  G (energy-momentum) ; as a consequence, spacetime geometry (the metric g  ) in part depends on matter, and in part it has its own wavelike dynamics. Is this the final word on gravity? Almost certainly not, because of quantum matter if nothing else. What about quantizing gravity itself? Ok, and we can perhaps guess what such a theory might tell us, but the first big question is, How? The most developed approaches are string theory and loop quantum gravity, but there are more radical ones.

4. the causal set approach Basic idea: A causal set is a discrete version of spacetime, stripped of everything except for the causal relationships x < y among its elements. Kinematics: To what extent is all of spacetime geometry encoded in the relations? Dynamics: Use for example the action Basic idea: A causal set is a discrete version of spacetime, stripped of everything except for the causal relationships x < y among its elements. Kinematics: To what extent is all of spacetime geometry encoded in the relations? Dynamics: Use for example the action

6. loop quantum gravity approach Type of approach: Apply canonical quantization to a version of classical general relativity in which spacetime = space  time, and choose an appropriate set of variables. The variables: The metric g  is split into spatial information, encoded in a triad of vectors E a i, and its conjugate “momentum”, a connection A a i for the rotation group. One then looks for wave functions  (A,t) satisfying a quantum version of Einstein’s equation. It turns out that important ones are based on graphs… Open questions: Many! From very technical ones to, What does it mean for this field to be made of quanta? What is time? … And also, … What do “semiclassical solutions” look like? Type of approach: Apply canonical quantization to a version of classical general relativity in which spacetime = space  time, and choose an appropriate set of variables. The variables: The metric g  is split into spatial information, encoded in a triad of vectors E a i, and its conjugate “momentum”, a connection A a i for the rotation group. One then looks for wave functions  (A,t) satisfying a quantum version of Einstein’s equation. It turns out that important ones are based on graphs… Open questions: Many! From very technical ones to, What does it mean for this field to be made of quanta? What is time? … And also, … What do “semiclassical solutions” look like?

7. some phenomenological questions Quanta of gravity: In principle they are somewhat like photons with a higher spin, but specific predictions are hard to make and we are not close to being able to detect them as particles. Cosmology: The big bang singularity, expansion, imprints on the CMB. Black holes: Singularities, entropy and Hawking radiation. Photons: Electromagnetic waves propagating in a vacuum satisfy, in Fourier transform space, the (no-) dispersion relation k 2 c 2 –  2 = 0, according to which n = 1. but quantum spacetime fluctuations are expected to change this. Is the effect observable? From dimensional analysis, one would think that corrections only appear at scales approaching Planck scales,  = l P = (Gh/c 3 ) 1/2 = 2  10 –33 cm  E P = (hc 5 /G) 1/2 = 1.3  10 19 GeV But there are loopholes... Quanta of gravity: In principle they are somewhat like photons with a higher spin, but specific predictions are hard to make and we are not close to being able to detect them as particles. Cosmology: The big bang singularity, expansion, imprints on the CMB. Black holes: Singularities, entropy and Hawking radiation. Photons: Electromagnetic waves propagating in a vacuum satisfy, in Fourier transform space, the (no-) dispersion relation k 2 c 2 –  2 = 0, according to which n = 1. but quantum spacetime fluctuations are expected to change this. Is the effect observable? From dimensional analysis, one would think that corrections only appear at scales approaching Planck scales,  = l P = (Gh/c 3 ) 1/2 = 2  10 –33 cm  E P = (hc 5 /G) 1/2 = 1.3  10 19 GeV But there are loopholes...