Melvin Magnetic Fluxtube/Cosmology Correspondence

1507.05534v2There are two basic ways that spatially extended magnetic fields are realized in general relativity –

  1. Static, gravitationally bound flux tubes
  2. Homogeneous, but anisotropic cosmologies

In our paper Jennie Traschen and I observed that the spacetime metrics associated with these two very different types of solutions are actually very closely related – mapping into one another via the interchange of time and space coordinates.  (This is very similar to what is known as the “domain wall/cosmology correspondence” in the context of AdS/CFT.)

We go on to explore various generalizations of the basic Melvin flux tube and magnetic cosmologies, examining how they interpolate at small and large cylindrical radii, or at early and late times, between different vacuum limits.


Symmetry Breaking Vacua in Lovelock Gravity

1506.01897v3Cetin Senturk (visiting UMass for a year) and I published a study of product vacua in Lovelock gravity.  Although Lovelock theories often have multiple maximally symmetric vacua (dS, AdS or flat) with different curvatures, there are In also regions of parameter space in which no maximally symmetric vacua exist.  These are symmetry breaking regions and the  boundary of these regions in parameter space signal phase transitions.

We created a survey (for 5, 6 and 7 dimensions) of vacua that are products of symmetric spaces, with an emphasis on symmetry breaking regions of parameter space.  In 5D, for example, we found that all of the symmetry breaking region is covered by product vacua, while in 6D there is still a portion of this region in which no such product vacua exists.

It would be interested to find a way to understand phase transitions between different Lovelock vacua in a dynamical sense.

Chemical Potential in the First Law for Holographic Entanglement Entropy

1409.3521Ryu & Takyanagi proposed that in AdS/CFT entanglement entropy of a region in the boundary field theory can be computed in terms of the area of a surface in the bulk, much like the formula for black hole entropy.  It has also been shown in earlier work, that holographic entanglement entropy satisfies a first law and that under certain circumstances the first law can be derived using techniques from black hole thermodynamics.

In our paper, Sourya Ray, Jennie Traschen and I showed how variation in the cosmological constant, whose contribution to BH thermodynamics we had studied in earlier work, enters the holographic first law as a chemical potential term that varies the number of degrees of freedom in the boundary QFT.

AdS Cosmologies

1407.4299Various 4D spacetimes can be studied in the context of AdS/CFT by embedding them on the Poincare slices of an asymptotically AdS spacetime.  In this paper, Sebastian Fischetti (former UMass undergrad!), Jennie Traschen and I showed how FRW cosmologies, including scalar and other types of matter fields, could be embedded on such slices.  We focussed on particular examples, where at late times the FRW cosmology approaches flat spacetime and examined how the entanglement entropy approached its equilibrium value in this limit.

Cosmological Magnetic Fluxtubes

1312.4923In this paper, Jennie Traschen and I have found solutions to Einstein-Maxwell theory (as well as some extensions thereof) that describe Melvin magnetic flux tubes embedded in expanding cosmological backgrounds.  It is common lore in cosmology that magnetic fields dilute along with the expansion of the universe.  We find that, while this may be true for uniformly spread out B-fields, it is not generally true for gravitationally bound flux tubes.  It would be interesting to know whether such flux tubes can be created in the early universe, e.g. during inflation, and play a role in the evolution of large scale B fields in our own universe.

See also our post about this article on the CQG+ blog.

Conformal Tensors via Lovelock Gravity

1306.4637I recently posted a paper that continues my investigation (begun in arXiv:1202.5287) into geometric properties of Lovelock gravity theories.  Lovelock theories are generalizations of Einstein gravity that include a unique term in the Lagrangian at each higher curvature order, singled out the property that the equations of motion continue to depend only on second (and no higher) derivatives of the metric.  In arXiv:1202.5287, I presented an nth order generalized version of the Riemann tensor, whose properties underly those of the nth order Lovelock term and discussed the special properties of these tensors in low dimensions, which parallel those of the Riemann curvature itself in D=2 and D=3.  In the most recent paper, I look focus on conformal tensors that generalize the Weyl, Schouten, Cotton and Bach tensors familiar from ordinary general relativity.

Link to arXiv version of paper.

Sum Rule for the ADM Mass and Tensions in Planar AdS Spacetimes

planar_bhBasem Mahmoud El-Manoufi, Ben Ett, Jennie Traschen and I have posted a short paper that provides a clear foundation for an observation made in our earlier paper arXiv:1302.6980.  There we established via bulk gravitational computations that for asymptotically planar AdS spacetimes the sum of the mass and gravitational tensions in the planar directions necessarily vanishes, a result that has long been known in the AdS/CFT context.  This very fundamental result was lacking a clear, intuitive explanation in our earlier work.  In this paper, we show that it follows via relatively simple Hamiltonian methods in GR applied to evolution along the Killing direction in AdS that generates scale transformations on the Lorentzian planar slices.

Link to arXiv version of paper.

Universality of Inner Black Hole Mechanics and Higher Curvature Gravity

1304.1696Alejandra Castro, Nima Dehmani, Gaston Giribet and I have posted a paper that addresses the issue of the quantization of the product of horizon entropies for black hole solutions in higher derivative gravity theories.  The history of this is that for black holes in Einstein gravity, such as the Kerr-Newman spacetime, the product of the inner and outer horizon areas depends only on the charge and angular momentum and not on the mass – i.e. quantities that will be quantized in a quantum mechanical treatment (see the e.g. discussions in arXiv:1011.0008 and arXiv:1204.1284).  In Einstein gravity, the black hole entropy is proportional to the horizon area.  However, in higher derivative theories this is no longer generally true (see gr-qc/9307038).  In such cases, one would expect the product of horizon entropies, which is the quantity of fundamental significance, to be independent of the mass, rather than the product of areas.  However, in the examples we study, we find the opposite to be true.

Link to arXiv version of paper.

Gravitational Tension and Thermodynamics of Planar AdS Spacetimes

1302.6980Basem Mahmoud El-Manoufi, Ben Ett, Jennie Traschen and I have studied the gravitational tension (originally introduced by Jennie and Dan Fox in gr-qc/0103106) for planar AdS spacetimes.  We derive a collection of Smarr formulas relating the mass and tensions in the planar directions to the black hole horizon area, Kaluza-Klein bubble surface area and the thermodynamic volume of the spacetime (which is conjugate to the variation of Λ in the first law).  A linear combination of these relations gives the vanishing of the sum of the mass and tensions, which corresponds to tracelessness of the boundary stress tensor in AdS/CFT.

Link to arXiv version of paper.


Thermodynamic Volumes and Isoperimetric Inequalities for de Sitter Black Holes

1301.5926Brian Dolan, David Kubiznak, Rob Mann, Jennie Traschen and I computed the thermodynamic volumes for a variety of different black hole solutions embedded in a background deSitter spacetime.  The thermodynamic volume had been identified in my earlier paper with Jennie and Sourya Ray (arXiv:0904.2765) as the potential conjugate to a varying cosmological constant in the first law of black hole thermodynamics.  Subsequent work by Kubiznak and collaborators (arXiv:1012.2888) showed that the thermodynamic volume for AdS black holes satisfied a “reverse isoperimetric inequality” with respect to the black hole horizon area.  We investigate this issue for deSitter black holes, where the important additional factor is the presence of the deSitter horizon, with its own thermodynamic volume.

Link to arXiv version of paper.