Rotating Black Holes in Higher Dimensions with a Cosmological Constant

We present the metric for a rotating black hole with a cosmological constant and with arbitrary angular momenta in all higher dimensions. The metric is given in both Kerr-Schild and Boyer-Lindquist form. In the Euclidean-signature case, we also obtain smooth compact Einstein spaces on associated S^{D-2} bundles over S^2, infinitely many for each odd D\ge 5. Applications to string theory and M-theory are indicated.Comment: 8 pages, Latex. Short version, with more compact notation, of hep-th/0404008. To appear in Phys. Rev. Let

Ultrahigh-throughput generation and characterization of cellular aggregates in laser-ablated microwells of poly(dimethylsiloxane)

Aggregates of cells, also known as multicellular aggregates (MCAs), have been used as microscale tissues in the fields of cancer biology, regenerative medicine, and developmental biology for many decades. However, small MCAs (fewer than 100 cells per aggregate) have remained challenging to manufacture in large quantities at high uniformity. Forced aggregation into microwells offers a promising solution for forming consistent aggregates, but commercial sources of microwells are expensive, complicated to manufacture, or lack the surface packing densities that would significantly improve MCA production. To address these concerns, we custom-modified a commercial laser cutter to provide complete control over laser ablation and directly generate microwells in a poly(dimethylsiloxane) (PDMS) substrate. We achieved ultra rapid microwell production speeds (>50000 microwells per h) at high areal packing densities (1800 microwells per cm2) and over large surface areas for cell culture (60 cm2). Variation of the PDMS substrate distance from the laser focal plane during ablation allowed for the generation of microwells with a variety of sizes, contours, and aspect ratios. Casting of high-fidelity microneedle masters in polyurethane allowed for non-ablative microwell reproduction through replica molding. MCAs of human bone marrow derived mesenchymal stem cells (hMSCs), murine 344SQ metastatic adenocarcinoma cells, and human C4-2 prostate cancer cells were generated in our system with high uniformity within 24 hours, and computer vision software aided in the ultra-high-throughput analysis of harvested aggregates. Moreover, MCAs maintained invasive capabilities in 3D migration assays. In particular, 344SQ MCAs demonstrated epithelial lumen formation on Matrigel, and underwent EMT and invasion in the presence of TGF-β. We expect this technique to find broad utility in the generation and cultivation of cancer cell aggregates, primary cell aggregates, and embryoid bodies

New Einstein-Sasaki and Einstein Spaces from Kerr-de Sitter

In this paper, which is an elaboration of our results in hep-th/0504225, we construct new Einstein-Sasaki spaces L^{p,q,r_1,...,r_{n-1}} in all odd dimensions D=2n+1\ge 5. They arise by taking certain BPS limits of the Euclideanised Kerr-de Sitter metrics. This yields local Einstein-Sasaki metrics of cohomogeneity n, with toric U(1)^{n+1} principal orbits, and n real non-trivial parameters. By studying the structure of the degenerate orbits we show that for appropriate choices of the parameters, characterised by the (n+1) coprime integers (p,q,r_1,...,r_{n-1}), the local metrics extend smoothly onto complete and non-singular compact Einstein-Sasaki manifolds L^{p,q,r_1,...,r_{n-1}}. We also construct new complete and non-singular compact Einstein spaces \Lambda^{p,q,r_1,...,r_n} in D=2n+1 that are not Sasakian, by choosing parameters appropriately in the Euclideanised Kerr-de Sitter metrics when no BPS limit is taken.Comment: latex, 26 page

Entropy of A Scalar Field In (3 + 1)-dimensional Taub-NUT Space-Time

In this article we discuss a few aspects of the space-time description of fields and particles. In sectionn II and III we demonstrate that fields are as fundamental as particles. In section IV we discuss non-equivalence of the Schwarzschild coordinates and the Kruskal-Szekeres coordinates. In section V we discuss that it is not possible to define causal structure in discrete space-time manifolds. In App.B we show that a line is not just a collection of points and we will have to introduce one-dimensional line-intervals as fundamental geometric elements. Similar discussions are valid for area and volume-elements. In App.C and App.D we make a comparative study of Quantum Field Theory and Quantum Mechanics and contradictions associated with probabilistics interpretation of these theories with space-time dimensional analysis. In App.E and App.F we discuss the geometry of Robertson-Walker model and electrostatic behavior of dielectrics respectively. In Sup.I we discuss the regularity of Spin-Spherical harmonics and also derive an energy-spectrum which is free of back-reaction problem. In Sup.II we discuss that in general the integral version of Gauss's divergence law in Electrodynamics is not valid and rederive Gauss's law and Ampere's law. We also show that under duality transformation magnetic charge conservation law do not remain time reversal symmetric. In Sup.III we derive the complete equation for viscous compressible fluids and make a few comments regarding some cotradictions associated with boundary conditions for fluid dynamics. In Sup.IV we discuss a few aspects on double slit interference experiments. We conclude this article with a few questions in Sup.V.Comment: Revtex, 26 pages, A few sections are adde

Thermal Particle Creation in Cosmological Spacetimes: A Stochastic Approach

The stochastic method based on the influence functional formalism introduced in an earlier paper to treat particle creation in near-uniformly accelerated detectors and collapsing masses is applied here to treat thermal and near-thermal radiance in certain types of cosmological expansions. It is indicated how the appearance of thermal radiance in different cosmological spacetimes and in the two apparently distinct classes of black hole and cosmological spacetimes can be understood under a unifying conceptual and methodological framework.Comment: 17 pages, revtex (aps, eqsecnum), submitted to PRD, April 199

Barn-Raising on the Digital Frontier: The L.A.U.N.C.H. Collaborative

A meta-analysis of oncology papers from around the world revealed that cancer patients who lived more than 50 miles away from hospital centers routinely presented with more advanced stages of disease at diagnosis, exhibited lower adherence to prescribed treatments, presented with poorer diagnoses, and reported a lower quality of life than patients who lived nearer to care facilities. Connected health approaches—or the use of broadband and telecommunications technologies to evaluate, diagnose, and monitor patients beyond the clinic—are becoming an indispensable tool in medicine to overcome the obstacle of distance

No-Bang Quantum State of the Cosmos

A quantum state of the entire cosmos (universe or multiverse) is proposed which is the equal mixture of the Giddings-Marolf states that are asymptotically single de Sitter spacetimes in both past and future and are regular on the throat or neck of minimal three-volume. That is, states are excluded that have a big bang or big crunch or which split into multiple asymptotic de Sitter spacetimes. (For simplicity, transitions between different values of the cosmological constant are assumed not to occur, though different positive values are allowed.) The entropy of this mixed state appears to be of the order of the three-fourths power of the Bekenstein-Hawking A/4 entropy of de Sitter spacetime. Most of the component pure states do not have rapid inflation, but when an inflaton is present and the states are weighted by the volume at the end of inflation, a much smaller number of states may dominate and give a large amount of inflation and hence may agree with observations.Comment: 18 pages, LaTeX, updated with a few new qualifications and reference

Susskind's Challenge to the Hartle-Hawking No-Boundary Proposal and Possible Resolutions

Given the observed cosmic acceleration, Leonard Susskind has presented the following argument against the Hartle-Hawking no-boundary proposal for the quantum state of the universe: It should most likely lead to a nearly empty large de Sitter universe, rather than to early rapid inflation. Even if one adds the condition of observers, they are most likely to form by quantum fluctuations in de Sitter and therefore not see the structure that we observe. Here I present my own amplified version of this argument and consider possible resolutions, one of which seems to imply that inflation expands the universe to be larger than 10^{10^{10^{122}}} Mpc.Comment: 24 pages, LaTeX, 8 references added and a distinction between Linde's and Vilenkin's tunneling proposal