Final answer:
A hash index can only handle simple equality comparisons by using a hash function to map keys to specific buckets. It is not suitable for range queries or sorting, unlike B-tree, BRIN, and GIN indexes which support more complex queries and data types.
Step-by-step explanation:
The type of index that can only handle simple equality comparisons is a hash index. Hash indexes work by applying a hash function to the key value of each entry and using the result as an index into an array of buckets or slots from which the desired value can be retrieved. This type of indexing is efficient for equality comparisons, for instance, when the query is of the form WHERE column = value. However, they are not suited for range queries or sorting as they do not store their entries in a sorted order.
In contrast, B-tree indexes support a broad range of queries, including range searches and sorting because they maintain their entries in a sorted structure. BRIN indexes (Block Range Indexes) are also efficient for queries that involve searching over ranges, particularly when dealing with large tables where values are physically stored close together. Finally, the GIN index (Generalized Inverted Index) is optimally used for indexing composite values where an item may contain multiple component values, such as arrays, and is good for handling cases with multiple values linked to an index record. These last three types of indexes support more than just simple equality comparisons.