{
  "id": "2104.02501",
  "version": "v1",
  "published": "2021-04-06T13:31:57.000Z",
  "updated": "2021-04-06T13:31:57.000Z",
  "title": "A Study On Some Geometric Properties and Physical Applications of A Mixed Quasi-Einstein Spacetime",
  "authors": [
    "Kaushik Chattopadhyay",
    "Arindam Bhattacharyya",
    "Dipankar Debnath"
  ],
  "comment": "28 pages. arXiv admin note: text overlap with arXiv:2101.11554",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In the present paper we discuss about a set of geometric properties and physical applications of a mixed quasi-Einstein spacetime$[M(QE)_{4}]$, which is a special type of nearly quasi-Einstein spacetime$[N(QE)_{4}]$. Firstly we consider a nearly quasi-Einstein manifold$[N(QE)_{n}]$ along with a mixed quasi-Einstein manifold$[M(QE)_{n}]$ and study some geometric conditions with respect to different curvature tensors on them. Then we consider a mixed quasi-Einstein spacetime and study $W_{2}$-Ricci pseudosymmetry and projective Ricci pseudosymmetry on it. Then we study the conditions $H \\cdot S=0$ and $\\tilde C \\cdot S=0$ in an $M(QE)_{4}$ spacetime, where $H, \\tilde C$ are the conharmonical curvature tensor and semiconformal curvature tensor respectively. Next we consider a semiconformally flat Ricci pseudosymmetric $M(QE)_{4}$ spacetime and find the nature of that spacetime. In the next section we study about some applications of a perfect fluid $M(QE)_{4}$ spacetime in the general theory of relativity. Followed by we discuss about the Ricci soliton structure in a semiconformally flat $M(QE)_{4}$ spacetime satisfying Einstein field equation without cosmological constant. Finally we give a nontrivial example of a $M(QE)_{4}$ spacetime to establish the existence of it.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-06T13:31:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C15",
      "53C25",
      "53C35"
    ],
    "keywords": [
      "mixed quasi-einstein spacetime",
      "geometric properties",
      "physical applications",
      "curvature tensor",
      "quasi-einstein manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}