964 research outputs found
The Lovelock gravity in the critical spacetime dimension
It is well known that the vacuum in the Einstein gravity, which is linear in
the Riemann curvature, is trivial in the critical (2+1=3) dimension because
vacuum solution is flat. It turns out that this is true in general for any odd
critical dimension where is the degree of homogeneous polynomial
in Riemann defining its higher order analogue whose trace is the nth order
Lovelock polynomial. This is the "curvature" for nth order pure Lovelock
gravity as the trace of its Bianchi derivative gives the corresponding analogue
of the Einstein tensor \cite{bianchi}. Thus the vacuum in the pure Lovelock
gravity is always trivial in the odd critical (2n+1) dimension which means it
is pure Lovelock flat but it is not Riemann flat unless and then it
describes a field of a global monopole. Further by adding Lambda we obtain the
Lovelock analogue of the BTZ black hole.Comment: 3 pages, revised version with two minor changes and an author added.
Accepted for publication in Physics Letters
A spacetime dual to the NUT spacetime
By decomposing the Riemann curvature into electric and magnetic parts, a
duality transformation, which involves interchange of active and passive
electric parts, has recently been proposed. It was shown that the Schwarzschild
solution is dual to the one that describes the Schwarzschild particle with
cloud of string dust or a global monopole. Following the same procedure we
obtain the solution dual to the NUT spacetime.Comment: 10 pages, Latex. Accepted for publication in Classical and Quantum
Gravit
Electromagnetic duality in general relativity
By resolving the Riemann curvature relative to a unit timelike vector into
electric and magnetic parts, we consider duality relations analogous to the
electromagnetic theory. It turns out that the duality symmetry of the Einstein
action implies the Einstein vacuum equation without the cosmological term. The
vacuum equation is invariant under interchange of active and passive electric
parts giving rise to the same vacuum solutions but the gravitational constant
changes sign. Further by modifying the equation it is possible to construct
interesting dual solutions to vacuum as well as to flat spacetimes.Comment: 18 pages, LaTEX versio
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