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Gravitation, Strings and Cosmology |
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Of all the fundamental forces (electromagnetism, gravitation, weak and strong nuclear forces), gravity remains the most mysterious. In spite of its remarkable successes, Einstein’s general theory of relativity, which has led to an unprecedented geometrization of physics, is an unfinished revolution. Research in mathematical physics will be pursued in areas related in the broadest sense to Einstein’s theory of gravitation (physics and mathematics). Quantum gravityTwo major achievements of early 20th century physics were the development of quantum mechanics and the discovery by Einstein of the theory of general relativity. The former describes the laws of physics at the smallest scales while the latter is the classical theory of gravity, which dominates physics at the largest scales. Both theories have been checked in numerous settings and with an astonishing accuracy. In view of this, it is highly surprising that both theories are found to be mutually incompatible: all attempts to quantize gravity along the lines that proved successful for the other forces lead to insurmountable difficulties (e.g. infinite probabilities). Reconciling general relativity with quantum mechanics is a challenge for the 21st century. A very promising avenue is string theory, in which the fundamental quanta are not point particles but extended objects. String theory realizes the old dream of Einstein of unifying all the forces and matter. Other interesting approaches to quantum gravity exist. All these indicate that our concepts of space and time (including the very notion of spacetime dimension) will have to be dramatically revised at the microscopic level. Black holesBlack holes – objects whose gravitational attraction is so strong that nothing, not even light, can escape from them – are probably the most fascinating objects predicted by general relativity. Recent astrophysical observations show them to be ubiquitous. Black holes might hold important clues to quantum gravity. Indeed, as shown by Hawking, black holes are not strictly black but radiate. The Hawking radiation results from the effect of the distorted black hole geometry on quantized fields and implies that black holes are characterized by a temperature and an entropy proportional to their area. A microscopic understanding of the black hole entropy is still lacking in the general case and will require a consistent description of gravity at the quantum level. The cosmological constant problemAccording to Einstein theory of gravity, every form of energy gravitates. In particular, the energy of the vacuum state of quantum field theories contributes to the gravitational field. This gravitational source takes the same form as the famous cosmological constant term added and then dropped by Einstein in his celebrated field equations. Attempts to compute the cosmological from microphysics gives a value … 120 orders of magnitude bigger than the observed value. This clearly indicates a fundamental misunderstanding, the resolution of which might hold many surprises. Mathematical aspectsGravity and mathematics have had close and fruitful ties since the very beginning (differential geometry, topology, Lie groups, infinite-dimensional algebras). Gravity exhibits also remarkable connections with dynamical systems (chaos, integrability). These ties are likely to deepen further in the future and to lead to fundamental developments in both physics and mathematics. Associated Research Teams Physique théorique et mathématique (ULB)
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